The investigator proposes to develop parallel methods for solving unconstrained optimization problems and to implement them on a 1024-processor hypercube such as the NCUBE 1 machine at the University of South Carolina. In particular, she proposes to parallelize those parts of the algorithm that are costly and where speedups are most useful, namely the linear algebra solution and updating. The PI wants to approach the problem by finding updating strategies for the Hessian on the basis of the type of linear equation solver used to find the direction dk. These would not include, for example, the factored or unfactored parallel versions of the BFGS method using either the Hessian or its inverse since these have already been parallelized. The PI would consider two methods for solving linear equations: a) the LU factorization or some variation of it, and b) an iterative method using multiple blocks. In summary, the PI would like to parallelize a quasi-Newton method for solving unconstrained optimization problems using LU updates and to find updating schemes for the Hessian where the Hessian is split into multiple blocks.
